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// $Id$
//
// Copyright (C) 2004-2013 Rational Discovery LLC
//
// @@ All Rights Reserved @@
// This file is part of the RDKit.
// The contents are covered by the terms of the BSD license
// which is included in the file license.txt, found at the root
// of the RDKit source tree.
//
#include "AngleBend.h"
#include "BondStretch.h"
#include "Params.h"
#include <math.h>
#include <ForceField/ForceField.h>
#include <RDGeneral/Invariant.h>
#include <RDGeneral/utils.h>
namespace ForceFields {
namespace UFF {
namespace Utils {
double calcAngleForceConstant(double theta0, double bondOrder12,
double bondOrder23, const AtomicParams *at1Params,
const AtomicParams *at2Params,
const AtomicParams *at3Params) {
double cosTheta0 = cos(theta0);
double r12 = calcBondRestLength(bondOrder12, at1Params, at2Params);
double r23 = calcBondRestLength(bondOrder23, at2Params, at3Params);
double r13 = sqrt(r12 * r12 + r23 * r23 - 2. * r12 * r23 * cosTheta0);
double beta = 2. * Params::G / (r12 * r23);
double preFactor = beta * at1Params->Z1 * at3Params->Z1 / int_pow<5>(r13);
double rTerm = r12 * r23;
double innerBit =
3. * rTerm * (1. - cosTheta0 * cosTheta0) - r13 * r13 * cosTheta0;
double res = preFactor * rTerm * innerBit;
return res;
}
void calcAngleBendGrad(RDGeom::Point3D *r, double *dist, double **g,
double &dE_dTheta, double &cosTheta, double &sinTheta) {
// -------
// dTheta/dx is trickier:
double dCos_dS[6] = {1.0 / dist[0] * (r[1].x - cosTheta * r[0].x),
1.0 / dist[0] * (r[1].y - cosTheta * r[0].y),
1.0 / dist[0] * (r[1].z - cosTheta * r[0].z),
1.0 / dist[1] * (r[0].x - cosTheta * r[1].x),
1.0 / dist[1] * (r[0].y - cosTheta * r[1].y),
1.0 / dist[1] * (r[0].z - cosTheta * r[1].z)};
g[0][0] += dE_dTheta * dCos_dS[0] / (-sinTheta);
g[0][1] += dE_dTheta * dCos_dS[1] / (-sinTheta);
g[0][2] += dE_dTheta * dCos_dS[2] / (-sinTheta);
g[1][0] += dE_dTheta * (-dCos_dS[0] - dCos_dS[3]) / (-sinTheta);
g[1][1] += dE_dTheta * (-dCos_dS[1] - dCos_dS[4]) / (-sinTheta);
g[1][2] += dE_dTheta * (-dCos_dS[2] - dCos_dS[5]) / (-sinTheta);
g[2][0] += dE_dTheta * dCos_dS[3] / (-sinTheta);
g[2][1] += dE_dTheta * dCos_dS[4] / (-sinTheta);
g[2][2] += dE_dTheta * dCos_dS[5] / (-sinTheta);
}
} // end of namespace Utils
AngleBendContrib::AngleBendContrib(ForceField *owner, unsigned int idx1,
unsigned int idx2, unsigned int idx3,
double bondOrder12, double bondOrder23,
const AtomicParams *at1Params,
const AtomicParams *at2Params,
const AtomicParams *at3Params,
unsigned int order) {
PRECONDITION(owner, "bad owner");
PRECONDITION(at1Params, "bad params pointer");
PRECONDITION(at2Params, "bad params pointer");
PRECONDITION(at3Params, "bad params pointer");
PRECONDITION((idx1 != idx2 && idx2 != idx3 && idx1 != idx3),
"degenerate points");
URANGE_CHECK(idx1, owner->positions().size());
URANGE_CHECK(idx2, owner->positions().size());
URANGE_CHECK(idx3, owner->positions().size());
// the following is a hack to get decent geometries
// with 3- and 4-membered rings incorporating sp2 atoms
double theta0 = at2Params->theta0;
if (order >= 30) {
switch (order) {
case 30:
theta0 = 150.0 / 180.0 * M_PI;
break;
case 35:
theta0 = 60.0 / 180.0 * M_PI;
break;
case 40:
theta0 = 135.0 / 180.0 * M_PI;
break;
case 45:
theta0 = 90.0 / 180.0 * M_PI;
break;
}
order = 0;
}
// end of the hack
dp_forceField = owner;
d_at1Idx = idx1;
d_at2Idx = idx2;
d_at3Idx = idx3;
d_order = order;
d_forceConstant = Utils::calcAngleForceConstant(
theta0, bondOrder12, bondOrder23, at1Params, at2Params, at3Params);
if (order == 0) {
double sinTheta0 = sin(theta0);
double cosTheta0 = cos(theta0);
d_C2 = 1. / (4. * std::max(sinTheta0 * sinTheta0, 1e-8));
d_C1 = -4. * d_C2 * cosTheta0;
d_C0 = d_C2 * (2. * cosTheta0 * cosTheta0 + 1.);
}
}
double AngleBendContrib::getEnergy(double *pos) const {
PRECONDITION(dp_forceField, "no owner");
PRECONDITION(pos, "bad vector");
double dist1 = dp_forceField->distance(d_at1Idx, d_at2Idx, pos);
double dist2 = dp_forceField->distance(d_at2Idx, d_at3Idx, pos);
RDGeom::Point3D p1(pos[3 * d_at1Idx], pos[3 * d_at1Idx + 1],
pos[3 * d_at1Idx + 2]);
RDGeom::Point3D p2(pos[3 * d_at2Idx], pos[3 * d_at2Idx + 1],
pos[3 * d_at2Idx + 2]);
RDGeom::Point3D p3(pos[3 * d_at3Idx], pos[3 * d_at3Idx + 1],
pos[3 * d_at3Idx + 2]);
RDGeom::Point3D p12 = p1 - p2;
RDGeom::Point3D p32 = p3 - p2;
double cosTheta = p12.dotProduct(p32) / (dist1 * dist2);
clipToOne(cosTheta);
// we need sin^2(theta) to get cos(2*theta), so compute that:
double sinThetaSq = 1. - cosTheta * cosTheta;
double angleTerm = getEnergyTerm(cosTheta, sinThetaSq);
double res = d_forceConstant * angleTerm;
return res;
}
void AngleBendContrib::getGrad(double *pos, double *grad) const {
PRECONDITION(dp_forceField, "no owner");
PRECONDITION(pos, "bad vector");
PRECONDITION(grad, "bad vector");
double dist[2] = {dp_forceField->distance(d_at1Idx, d_at2Idx, pos),
dp_forceField->distance(d_at2Idx, d_at3Idx, pos)};
RDGeom::Point3D p1(pos[3 * d_at1Idx], pos[3 * d_at1Idx + 1],
pos[3 * d_at1Idx + 2]);
RDGeom::Point3D p2(pos[3 * d_at2Idx], pos[3 * d_at2Idx + 1],
pos[3 * d_at2Idx + 2]);
RDGeom::Point3D p3(pos[3 * d_at3Idx], pos[3 * d_at3Idx + 1],
pos[3 * d_at3Idx + 2]);
double *g[3] = {&(grad[3 * d_at1Idx]), &(grad[3 * d_at2Idx]),
&(grad[3 * d_at3Idx])};
RDGeom::Point3D r[2] = {(p1 - p2) / dist[0], (p3 - p2) / dist[1]};
double cosTheta = r[0].dotProduct(r[1]);
clipToOne(cosTheta);
double sinThetaSq = 1.0 - cosTheta * cosTheta;
double sinTheta =
std::max(((sinThetaSq > 0.0) ? sqrt(sinThetaSq) : 0.0), 1.0e-8);
// std::cerr << "GRAD: " << cosTheta << " (" << acos(cosTheta)<< "), ";
// std::cerr << sinTheta << " (" << asin(sinTheta)<< ")" << std::endl;
// use the chain rule:
// dE/dx = dE/dTheta * dTheta/dx
// dE/dTheta is independent of cartesians:
double dE_dTheta = getThetaDeriv(cosTheta, sinTheta);
Utils::calcAngleBendGrad(r, dist, g, dE_dTheta, cosTheta, sinTheta);
}
double AngleBendContrib::getEnergyTerm(double cosTheta,
double sinThetaSq) const {
PRECONDITION(d_order == 0 || d_order == 1 || d_order == 2 || d_order == 3 ||
d_order == 4,
"bad order");
// cos(2x) = cos^2(x) - sin^2(x);
double cos2Theta = cosTheta * cosTheta - sinThetaSq;
double res = 0.0;
if (d_order == 0) {
res = d_C0 + d_C1 * cosTheta + d_C2 * cos2Theta;
} else {
switch (d_order) {
case 1:
res = -cosTheta;
break;
case 2:
res = cos2Theta;
break;
case 3:
// cos(3x) = cos^3(x) - 3*cos(x)*sin^2(x)
res = cosTheta * (cosTheta * cosTheta - 3. * sinThetaSq);
break;
case 4:
// cos(4x) = cos^4(x) - 6*cos^2(x)*sin^2(x)+sin^4(x)
res = int_pow<4>(cosTheta) - 6. * cosTheta * cosTheta * sinThetaSq +
sinThetaSq * sinThetaSq;
break;
}
res = 1. - res;
res /= (double)(d_order * d_order);
}
return res;
}
double AngleBendContrib::getThetaDeriv(double cosTheta, double sinTheta) const {
PRECONDITION(d_order == 0 || d_order == 1 || d_order == 2 || d_order == 3 ||
d_order == 4,
"bad order");
double dE_dTheta = 0.0;
double sin2Theta = 2. * sinTheta * cosTheta;
if (d_order == 0) {
dE_dTheta =
-1. * d_forceConstant * (d_C1 * sinTheta + 2. * d_C2 * sin2Theta);
} else {
// E = k/n^2 [1-cos(n theta)]
// dE = - k/n^2 * d cos(n theta)
// these all use:
// d cos(ax) = -a sin(ax)
switch (d_order) {
case 1:
dE_dTheta = -sinTheta;
break;
case 2:
// sin(2*x) = 2*cos(x)*sin(x)
dE_dTheta = sin2Theta;
break;
case 3:
// sin(3*x) = 3*sin(x) - 4*sin^3(x)
dE_dTheta = sinTheta * (3. - 4. * sinTheta * sinTheta);
break;
case 4:
// sin(4*x) = cos(x)*(4*sin(x) - 8*sin^3(x))
dE_dTheta = cosTheta * sinTheta * (4. - 8. * sinTheta * sinTheta);
break;
}
dE_dTheta *= d_forceConstant / (double)(d_order);
}
return dE_dTheta;
}
}
}
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